math-calculus

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|2x+1|-|x-2| = 2
i not get how to do this cause everything on one side i never did these question like this before.

  • math-calculus -

    how about starting like this

    |2x+1| = |x+2| +2
    2x+1 = |x+2| +2 or -2x-1 = |x+2|+2
    |x+2|= 2x -1 or |x+2| = -2x-3

    now again.

    x+2 = 2x-1 or -x-2 = 2x-1, where 2x+1>0 --> x>-1/2
    x = 3 or x=-1/3

    or

    x+2= -2x-3 or -x-2 = -2x-3 , where -2x-3>0 -->x <-3/2
    3x=-5 or x = -1
    x = -5/3 or x = -1
    so x = -1 does not satisfy the condition

    x=3 , -1/3 , -5/3 are possible solutions

    testing each one in the original showed me that -1/3 does not work, so

    x = 3, x = -5/3

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